Calculating Car Distribution and Differences Across States

The problem provides data about the distribution of cars across four different states (A, B, C, and D) and the ratio of diesel to petrol engine cars within each state. We are given the total number of cars across all states and the percentage distribution for each state.

Total number of cars in all four states = 1400.

The table shows the following data:

We need to find the difference between the number of diesel engine cars in State 'B' and the number of petrol engine cars in State 'D'.

Step 1: Calculate the total number of cars in State B

The percentage distribution of cars in State B is 28% of the total cars.

Total cars in State B = Total cars × Percentage distribution for State B

\text{Total cars in State B} = 1400 \times \frac{28}{100}

\text{Total cars in State B} = 14 \times 28

\text{Total cars in State B} = 392

So, there are 392 cars in State B.

Step 2: Calculate the number of diesel engine cars in State B

In State B, the ratio of diesel engine cars to petrol engine cars is 5 ∶ 9. This means that for every 5 diesel cars, there are 9 petrol cars. The total ratio parts are $5 + 9 = 14$.

Number of diesel cars in State B = (Ratio part for Diesel / Total ratio parts) × Total cars in State B

\text{Number of diesel cars in State B} = \frac{5}{14} \times 392

\text{Number of diesel cars in State B} = 5 \times \frac{392}{14}

\text{Number of diesel cars in State B} = 5 \times 28

\text{Number of diesel cars in State B} = 140

So, there are 140 diesel engine cars in State B.

Step 3: Calculate the total number of cars in State D

The percentage distribution of cars in State D is 26% of the total cars.

Total cars in State D = Total cars × Percentage distribution for State D

\text{Total cars in State D} = 1400 \times \frac{26}{100}

\text{Total cars in State D} = 14 \times 26

\text{Total cars in State D} = 364

So, there are 364 cars in State D.

Step 4: Calculate the number of petrol engine cars in State D

In State D, the ratio of diesel engine cars to petrol engine cars is 1 ∶ 1. This means the number of diesel cars is equal to the number of petrol cars. The total ratio parts are $1 + 1 = 2$.

Number of petrol cars in State D = (Ratio part for Petrol / Total ratio parts) × Total cars in State D

\text{Number of petrol cars in State D} = \frac{1}{2} \times 364

\text{Number of petrol cars in State D} = 182

So, there are 182 petrol engine cars in State D.

Step 5: Calculate the difference

We need to find the difference between the number of diesel engine cars in State B and the number of petrol engine cars in State D.

Difference = |Number of diesel cars in State B - Number of petrol cars in State D|

\text{Difference} = |140 - 182|

\text{Difference} = |-42|

\text{Difference} = 42

The difference between the number of diesel engine cars in State B and the number of petrol engine cars in State D is 42.

Revision Table: Key Calculations

Difference = Diesel cars in B - Petrol cars in D = $140 - 182 = -42$. The absolute difference is 42.

Additional Information: Data Interpretation

This problem involves interpreting data presented in a table. It requires understanding how to use percentage distributions to find absolute numbers from a total and how to use ratios to divide a quantity into parts. Data interpretation questions often combine different mathematical concepts like percentages, ratios, and basic arithmetic. Practicing these types of questions helps in developing skills for analyzing and drawing conclusions from given data sets. Pay close attention to what specific values are being asked for, such as the number of diesel cars vs. petrol cars in a particular state.